Square Root Calculator › Square root of 249
Square Root of 249
√249 ≈ 15.779734
249 is not a perfect square, so √249 is an irrational number that is approximately 15.779734. In simplified radical form, √249 = √249.
√249 lies between √225 = 15 and √256 = 16.
| Number | 249 |
| Square root (decimal) | 15.779734 |
| Simplified radical | √249 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 249
249 = 3 × 83. This is what determines the simplified radical: for √249 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √249 is already in simplest radical form as √249.
Estimating √249 by hand
√249 falls between √225 = 15 and √256 = 16, so it starts at 15.something. The Babylonian method refines that guess by averaging it with 249 ÷ the guess:
| Step | Estimate |
| Start | 15 |
| Step 1 | 15.8 |
| Step 2 | 15.779747 |
| Step 3 | 15.779734 |
After 3 steps the estimate is 15.779734, matching √249 ≈ 15.779734.
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Frequently asked questions
Is 249 a perfect square?
No, 249 is not a perfect square, so its square root is irrational and approximately 15.779734.
What is the square root of 249 in simplest radical form?
√249 = √249 in simplest radical form.